write linesr inequalities to represent the numbers of each fruit in a basket

Question

Baskets of fruit are being prepared to sell, each basket contains at least 8 apples and more than 4 oranges. Apples cost $0.25 each, and oranges cost $0.40 each. The budget allows no more than $6 in total for each basket. Let x represent the number of apples. Let y represent the number of oranges. Write linear inequalities to represent the numbers of each fruit in a basket

Answer 1

Linear Inequalities are usually easier to understand if you put them in full sentences before adding the the mathematical terms. Another tip to remember is that the inequality sign looks like an open mouth; the mouth always faces the greater quantity. 5>4 can be read as 5 is greater than 4 and x>4 can be read as x is greater than 4. 

 

For example, in the problem above you know that each apple costs $0.25 and each orange costs $0.40. You have a total of $6.00 so your purchase has to be either less than $6 or equal to $6.

 

25 cents times each apple plus 40 cents times each orange has to be less than or equal to 6 dollars. 

 

0.25x + 0.40y ≤6

 

Now, you also know the number of applies is greater than or equal to 8

 

x≥8

 

The same concept applies for the oranges. We know that there are greater than 4 oranges in each basket ("not greater than or equal to 4" in this case because the problem says more than)

 

y>4

 

Hope that helps!